Simplify the following expression: $n = \dfrac{-32x^2 + 40x}{8x^2 + 8x}$ You can assume $x \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-32x^2 + 40x = - (2\cdot2\cdot2\cdot2\cdot2 \cdot x \cdot x) + (2\cdot2\cdot2\cdot5 \cdot x)$ The denominator can be factored: $8x^2 + 8x = (2\cdot2\cdot2 \cdot x \cdot x) + (2\cdot2\cdot2 \cdot x)$ The greatest common factor of all the terms is $8x$ Factoring out $8x$ gives us: $n = \dfrac{(8x)(-4x + 5)}{(8x)(x + 1)}$ Dividing both the numerator and denominator by $8x$ gives: $n = \dfrac{-4x + 5}{x + 1}$